We implement Ti-Lin atop the state-of-the-art robustness veriﬁcation framework CNN-Cert [1]}. We evaluate it with neural networks trained on MNIST, CIFAR-10, and Tiny ImageNet datasets. For CNNs with Sigmoid/Tanh/Arctan functions, experimental results reveal that VeriNet [2]} is superior to DeepCert [3]} in 78.33% cases and Ti-Lin outperforms these two state-of-the-art techniques in 96.67% cases. Furthermore, Ti-Lin outperforms Newise, which is Network-wise Tightest approach with up to 63.70% improvement to certified robustness bounds. For CNNs with Maxpooling function, Ti-Lin outperforms CNN-Cert [1]} and DeepPoly [5]} with up to 235.54%, 43.14% improvement to certified robustness bounds, respectively. Finally, we conduct Wilcoxon rank-sum test [6]} and the results confirm that Ti-Lin significantly outperform the five state-of-the-art baseline methods in precision with the same time consumption.
